Like everyone else, I agree you should communicate your non intent immediately.

If I was on the recieving end of the email and got an email that discussed the training and was CC to the person doing the training, I would assume (and reasonably so) that the training was happening. If I got another email quickly (within a day) from the trainer saying they weren't doing the training, I would chalk it up to a miscommunication and go about my day.

BUT if I took that information and made up a schedule and planned on the training and THEN heard from the trainer that they weren't available, I would put most of the blame on the trainer for not letting me know beforehand.

Yes, it's rude to volunteer someone without checking, but it's also rude to allow incorrect information to inconvenience others when a simple 1 minute email could sort everything out BEFORE there is an issue.